Question

A black body at $227{}^{\circ }\text{C}$ radiates heat at the rate of $7{\text{cal/cm}}^2\text{s}$. At a temperature of $727{}^{\circ }\text{C}$, the rate of heat radiated in the same unit will be -

• A. $50{\text{cal/cm}}^2\text{s}$
• B. $112{\text{cal/cm}}^2\text{s}$
• C. $80{\text{cal/cm}}^2\text{s}$
• D. $60{\text{cal/cm}}^2\text{s}$

Answer 1

The correct option is B $112{\text{cal/cm}}^2\text{s}$

Given,
$T_1=227{}^{\circ }\text{C}=500\text{K}$
$T_2=727{}^{\circ }\text{C}=1000\text{K}$
Radiation, $R_1=7{\text{cals/cm}}^2\text{s}$

As we know by Stefan-Boltzman's law,
Radiation, $R\propto T^4$

So, $\frac{R_1}{R_2}={\left(\frac{T_1}{T_2}\right)}^4$
$\frac{7}{R_2}={\left(\frac{500}{1000}\right)}^4$

$R_2=112{\text{cals/cm}}^2\text{s}$